where \(\delta _j=\kappa _j \sqrt{4-\kappa _j^2}/2\) , \(V_{Hj}=2\delta _j\left[\alpha _2-\alpha _4(\kappa _j^2-6)\right]\) , \(x_{sj}=(x-x_j)\)  and \(t_{sj}=(t-t_j)\)  with \(x_j\)  and \(t_j\)  being translations along \(x\)  and \(t\)  axes. Modulation frequencies \(\kappa _1\)  and \(\kappa _2\)  are two independent free parameters that play key roles in the mutual interaction between the breathers. Depending on the parameter \(\kappa _j\) , Eq.(REF ) may represent either the superposition two fundamental AB or KM solitons [1]}. When \(\alpha _4=0\) , the solution reduces to the standard NLSE two breather solution Eq.(REF ) presented in [2]}, [3]}. For convenience, growth-rates of Eq.(REF ) can be given as:
\(V_{H1} & = & 2\delta _1\left[\alpha _2-\alpha _4(\kappa _1^2-6)\right]\\V_{H2} & = & 2\delta _2\left[\alpha _2-\alpha _4(\kappa _2^2-6)\right] \\\nonumber \) 
